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If R is an integral domain with unit element, prove that any unit in R[x] must already be a unit in R.

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Modern Algebra
Ring Theory (XL)
Polynomial Rings over Commutative rings
Integral Domain
Unit Element
Unit of a Commutative Ring

If R is an integral domain with unit element, prove that any unit in R[x] must already be a unit in R.

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This solution is comprised of a detailed explanation of Polynomial Rings over Commutative Rings.It contains step-by-step explanation that if R is an integral domain with unit element, then any unit in R[x] must already be a unit in R.

Solution contains detailed step-by-step explanation.

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See Also This Related BrainMass Solution

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

Modern Algebra
Ring Theory (XLI)
Polynomial Rings over Commutative rings
Integral Domain
Unit Element
Unit of a Commutative Ring

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

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